用几何动力学方法无监督求解电力潮流，速度快且物理一致。
Physics-Constrained Neural Dynamics: A Unified Manifold Framework for Large-Scale Power Flow Computation
- 将潮流方程转为流形上的梯度流，通过能量函数找平衡点。
- 无需标注数据，直接最小化物理残差，实现端到端物理约束学习。
- 适合大规模电力系统实时计算，尤其适合需要高物理保真的场景。
潮流分析是电力系统分析、规划与运行控制的基础工具。传统牛顿-拉夫逊法存在初值敏感和批量计算效率低的问题，而现有基于深度学习的潮流求解器多依赖有监督学习，需预先求解大量案例，难以保证物理一致性。本文提出一种基于流形几何与梯度流的神经物理潮流求解方法：将潮流方程描述为约束流形，构建能量函数 $V(oldsymbol{x}) = \frac{1}{2}\|\boldsymbol{F}(\boldsymbol{x})\|^2$ 及梯度流 $\frac{d\boldsymbol{x}}{dt} = -\nabla V(\boldsymbol{x})$，将潮流求解转化为动力系统平衡点寻找问题。神经网络通过无监督方式直接最小化物理残差进行训练，无需标签数据，实现了真正的“端到端”物理约束学习。
原文摘要 · Abstract (English)
Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation, while existing deep learning-based power flow solvers mostly rely on supervised learning, requiring pre-solving of numerous cases and struggling to guarantee physical consistency. This paper proposes a neural physics power flow solving method based on manifold geometry and gradient flow, by describing the power flow equations as a constraint manifold, and constructing an energy function \(V(\mathbf{x}) = \frac{1}{2}\|\mathbf{F}(\mathbf{x})\|^2\) and gradient flow \(\frac{d\mathbf{x}}{dt} = -\nabla V(\mathbf{x})\), transforming power flow solving into an equilibrium point finding problem for dynamical systems. Neural networks are trained in an unsupervised manner by directly minimizing physical residuals, requiring no labeled data, achieving true "end-to-end" physics-constrained learning.
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